Study of scalar meson a_0(980) from B→a_0(980)π decays

In this paper,we calculate the branching ratios and the direct CP-violating asymmetries for decays B0 →a00(980)π0,a0+(980)π-,a0-(980)π+ and B- →a00(980)π-,a0-(980)π0 by employing the perturbative QCD(pQCD) factorization approach at the leading order.We found that(a) the pQCD predictions for the branching ratios are around(0.4-2.8)×10-6,consistent with currently available experimental upper limits;(b) the CP asymmetries of B0 →a00(980)π0 and B- →a0-(980)π0 decays can be large,about(70-80)% for α=100-.     

Twist-three fragmentation function contribution to the single spin asymmetry in pp collisions

We study the twist-three fragmentation function contribution to the single transverse spin asymmetries in inclusive hadron production in pp   collisions, p^↑p→h+X$p^{\uparrow }p\to h+X$. In particular, we calculate the associated derivative terms which dominate the spin asymmetries in these processes. With certain parameterizations for the twist-three fragmentation function, we estimate its contribution to the single spin asymmetry of π⁰${\pi }^0$ production at RHIC energy. We find that the contribution is sizable and might be responsible for the big difference between the asymmetries in η   and π⁰${\pi }^0$ productions observed by the STAR collaboration at RHIC.     

Edge‐transitive homogeneous factorizations of complete uniform hypergraphs

For a finite set V and a positive integer k with , letting be the set of all k‐subsets of V, the pair is called the complete k‐hypergraph on V, while each k‐subset of V is called an edge. A factorization of the complete k‐hypergraph of index , simply a ‐factorization of order n, is a partition of the edges into s disjoint subsets such that each k‐hypergraph , called a factor, is a spanning subhypergraph of . Such a factorization is homogeneous if there exist two transitive subgroups G and M of the symmetric group of degree n such that G induces a transitive action on the set and M lies in the kernel of this action. In this article, we give a classification of homogeneous factorizations of that admit a group acting transitively on the edges of . It is shown that, for and , there exists an edge‐transitive homogeneous ‐factorization of order n if and only if is one of (32, 3, 5), (32, 3, 31), (33, 4, 5), , and , where and q is a prime power with .     

Rotational tools for factor analytic models

Rotational ambiguity is a major problem in the application of factor analysis to a variety of multivariate mixture resolution problems and particularly important in the analysis of environmental data. As part of the development of an implementation of positive matrix factorization for the U.S. Environmental Protection Agency to distribute in support of airborne particle source identification and apportionment, several tools have been developed to control the rotations and explore the extent of rotational solution space. This discussion of the nature of the rotational tools provides an understanding of these rotational tools as well as the basis for their incorporation into other implementations of least‐squares based solutions to the factor analysis problem. Several example algorithms are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Enclosings of decompositions of complete multigraphs in 2‐factorizations

Let k, m, n, λ, and μ be positive integers. A decomposition of into edge‐disjoint subgraphs is said to be enclosed by a decomposition of into edge‐disjoint subgraphs if and, after a suitable labeling of the vertices in both graphs, is a subgraph of and is a subgraph of for all . In this paper, we continue the study of enclosings of given decompositions by decompositions that consist of spanning subgraphs. A decomposition of a graph is a 2‐factorization if each subgraph is 2‐regular and spanning, and is Hamiltonian if each subgraph is a Hamiltonian cycle. We give necessary and sufficient conditions for the existence of a 2‐factorization of that encloses a given decomposition of whenever and . We also give necessary and sufficient conditions for the existence of a Hamiltonian decomposition of that encloses a given decomposition of whenever and either or and , or , , and .     

Positive solutions for boundary value problems of second order difference equations and their computation

We consider the following two classes of second order boundary value problems for difference equation:

     

On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems

In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, we present block SSOR and modified block SSOR iteration methods based on the special structures of the coefficient matrices. In each step of the block SSOR iteration, we employ the block LU factorization to solve the sub-systems of linear equations. We show that the block LU factorization is existent and stable when the coefficient matrices are block diagonally dominant of type-II by columns. Under suitable conditions, we establish convergence theorems for both block SSOR and modified block SSOR iteration methods. In addition, the block SSOR iteration and AF-ADI method are considered as preconditioners for the nonsymmetric systems of linear equations. Numerical experiments show that both block SSOR and modified block SSOR iterations are feasible iterative solvers and they are also effective for preconditioning Krylov subspace methods such as GMRES and BiCGSTAB when used to solve this class of systems of linear equations.     

On Finite Factorization Rings

Let R be a commutative ring with identity. R is a finite factorization ring (FFR) if every nonzero nonunit of R has only a finite number of factorizations up to order and associates. In this article, we give a characterization of R for R[X] and R[[X]] to be an FFR.     

Cluster Categories Coming from Cyclic Posets

Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable category of a Frobenius category is always triangulated and has a cluster structure in many cases. The continuous cluster categories of [14 Igusa , K. , Todorov , G. ( 2013 ). Continuous Frobenius categories . Proceedings of the Abel Symposium 2011 : 115 – 143 .[Crossref] , [Google Scholar]], the infinity-gon of [12 Holm , T. , Jøot rgensen , P. ( 2012 ). On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon . Math. Z. 270 : 277 – 295 .[Crossref], [Web of Science ®] , [Google Scholar]], and the m-cluster category of type A _∞ (m ≥ 3) [13 Holm , T. , Jøot rgensen , P. ( 2015 ). Cluster tilting vs. weak cluster tilting in Dynkin type A infinity . Forum Math. 27 : 1117 – 1137 .[Crossref], [Web of Science ®] , [Google Scholar]] are examples of this construction as well as some new examples such as the cluster category of ?². An extension of this construction and further examples are given in [16 Igusa, K., Todorov, G. Continuous Cluster Categories of Type D. arXiv:1309.7409 . [Google Scholar]].     

矩阵LU分解定理的简单证明及其数值实现

用简单的方法证明了矩阵LU分解定理,讨论了定理的推广以及定理相应的数值实现,并对《数值分析》课程教学方法改革进行了思考.